Fibonacci game

ABSTRACT

A game of skill and chance for one or more players which utilizes a single set of numbered pieces. Each number on each piece corresponds to a number in the Fibonacci series, for example: 8, 13, 21, 34, 55 and 89 or a similar series: 2, 3, 5, 8, 13 and 21 where each number is equal to the sum of the prior two numbers. Individual game pieces are identified by a number and a corresponding color and may also be of a corresponding size. A player obtains a game piece at each turn without knowing which numbered piece will be received. A player assembles groups of pieces on a game board or on a play area during and between turns with the objective of collecting six groups of numbers that add to the highest number in the series with each group starting with one number in the series being employed in the game. A player&#39;s game is completed when the six groups have been assembled. Players compete with each other to finish first, each player taking a piece from the shared set in turn. A player, when playing alone, can compete against the clock or attempt to complete the six groups in a minimum of plays. The game can be played with tiles, playing cards or on a computer, a smartphone or a tablet.

CROSS-REFERENCE TO RELATED APPLICATIONS

Not Applicable

FEDERALLY SPONSORED RESEARCH

Not Applicable

SEQUENCE LISTING OR PROGRAM

Not Applicable

BACKGROUND

I. Field of the Present Invention

This application relates to games combining skill and chance that incorporate the Fibonacci series or Golden Ratio and can be played by one or more players with game pieces and a game board or with playing cards or on a computer, smartphone or tablet.

II. Description and Examples of Prior Art

There are a great many games for one or more players that use a pack of cards where each player is dealt a “hand” of cards, players take cards from a shuffled pack or off the table and then collect sets of cards which are laid down on the playing table. These games can utilize classical card sets with suits of diamonds, hearts, clubs and spades or special sets of cards specific to the game. Many of these games can be played on a computer, smartphone or tablet. Other games are played using a game board and sets of pieces and may involve the rolling of a dice or taking game pieces “blind” from a bag during a players turn.

Games and mathematical teaching apparatus have been developed with components identified by a number from the Fibonacci series. The Fibonacci series, named after Leonardo Fibonacci a 12^(th) century mathematician, is an infinite series of numbers, specifically: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, . . . where each number is equal to the sum of the two prior numbers. The ratio of one number to the preceding number, for example 144/89, is the Golden Ratio or Phi and approaches 1.618 as the Fibonacci series grows longer.

The Golden Ratio first appeared in Euclid's Elements written around 350 BC. The Fibonacci numbers first appeared in a work written in ancient India sometime between 450 and 200 BC. The connection between the Fibonacci series and the Golden Ratio was first verified in the nineteenth century.

The Fibonacci numbers appear in nature more often than would be expected from pure chance, for example in the number of petals on different flowers. The Fibonacci series and the Golden Ratio are used in art and architecture and have many fascinating mathematical properties. The Golden Ratio is considered to be aesthetically pleasing and a link between nature and the arts.

Sabin in U.S. Pat. No. 6,575,756 (2003) discloses a set of blocks as an aid to teaching mathematical concepts in which blocks of different sizes are provided with dimensions that bear a relationship to numbers in the Fibonacci series. The blocks help teach the relationships between mathematics and disciplines such as biology, botany and architecture. The blocks are arranged and rearranged in a holding tray by the students and teacher.

Stone in U.S. Pat. No. 4,129,302 (1978) discloses a game requiring two sets of pieces with lengths corresponding to consecutive numbers in the Fibonacci series. An apparatus in the form of a translucent tube is adapted to receive the pieces. Each player in turn lays selected pieces end to end in the tube creating an ever lengthening column attempting to force the other player to reach or exceed a chosen mark on the tube.

Brown in US Patent Application 2010/0127454 (2010) discloses a game of strategy involving game pieces that are dividable into smaller game pieces and are of two colors. The game pieces are arranged in a pattern on a playing surface and divided into legal shapes in the course of play as each player attempts to develop a winning pattern defined by the rules of the game.

Cuisinaire Rods are a mathematical training aid used by elementary school teachers. The rods are of different lengths and colors. The smallest rod can be a cube 1 cm in the three dimensions. A set of rods have lengths of 1, 2, 3, 4, 5, 6, etc. The odd-numbered lengths may have cold colors and the even-numbered lengths may have warm colors. George Cuisinaire, a Belgian school teacher, invented the system and published a book on their use in 1952 with the name Les nombres en couleurs.

A card game for two players, called Fib-Fibonacci employs a deck of twenty-six playing cards selected from a conventional pack, specifically 2 jokers, 4 each of twos, threes, fives, sevens and eights. Each player begins with a hand of five cards and the remaining cards are the draw pile. Players alternate turns and during a turn either draw a card from the draw pile or play a card onto the table to start or add to a run. The first run is started with a joker and a run can go in two directions from the joker. The second card played on the joker must be a two or a three. The first two cards in a run will be 2-3, 2-5 or 3-5. A card may be played as the third or fourth card in a run only if the sum of the previous two cards in the run are equal to the cards value. It is that rule that connects the game to the Fibonacci series. Runs generally do not reach beyond four cards. The winner is the first person to get rid of all of his cards.

A concensus based technique called Planning Poker or Scrum-Poker has been used to estimate effort or relative size of tasks in software development. One version of the technique uses a deck of cards with numbers of the Fibonacci series specifically: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89. The reason for using the Fibonacci series is to reflect the inherent uncertainty in estimating large items. This is not a game.

The devices and games of the prior art do not combine the mathematical progression and aesthetic patterns and ratio of the Fibonacci series in a way which is simple, entertaining and educational. A Fibonacci based game system which meets these objectives has been invented and will now be described.

SUMMARY

A game of skill and chance for one or more players which utilizes a single set of pieces and a place where the pieces are assembled into groups, following the rules of the game. The game pieces are each identified by a number and a corresponding color and may also be of a size relative to the number. Each number on each piece corresponds to a number in the Fibonacci series or a modified Fibonacci series, where each number is equal to the sum of the prior two lower numbers for example: 8, 13, 21, 34, 55 and 89 or 2, 3, 5, 8, 13, and 21. A set of pieces for up to four players might consist of eighty-nine pieces. The objective is to collect groups of pieces where the numbers on the pieces in the group add to the largest number in the series. In the above example series, six groups have to be assembled each starting with a number in the series. A group may have many pieces or only one piece (the largest number piece in the set). A game is completed when one player has assembled all of the groups. Players compete with each other to finish first, each player taking a piece from the shared set in turn. A player, when playing alone, can compete against the clock or attempt to complete all of the groups with a minimum of plays.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1—a bar chart of the Fibonacci series.

FIG. 2—a bar chart of the Fibonacci series with additional stacked bars or tiles.

FIG. 3—a Fibonacci bar chart area completely filled with stacked tiles.

FIG. 4—a Fibonacci bar chart area completely filled with the maximum number of tiles.

FIG. 5—a Fibonacci bar chart area completely filled with the minimum number of tiles.

FIG. 6—six tiles used in the game.

FIG. 7—a means or apparatus for selecting a tile with an equal probability for each color.

FIG. 8—a means or apparatus for selecting a tile with an unequal probability for each color.

FIG. 9—a Fibonacci Game Board.

FIG. 10—a Fibonacci Game Board Screen on a computer, smartphone or tablet.

FIG. 11—six cards in a Fibonacci game card pack.

FIG. 12—six base cards in a Fibonacci game card pack.

FIG. 13—a bonus card in a Fibonacci game card pack.

FIG. 14—a design for the back of Fibonacci game cards.

DRAWINGS Reference Numerals

-   1. a tile for Fibonacci number 8. -   2. a tile for Fibonacci number 13. -   3. a tile for Fibonacci number 21. -   4. a tile for Fibonacci number 34. -   5. a tile for Fibonacci number 55. -   6. a tile for Fibonacci number 89. -   7. a rotating pointer in a tile selecting device. -   8. color segments of equal size in a tile selecting device. -   9. color segments of unequal size in a tile selecting device. -   10. the recessed playing area in a game board. -   11. diagram of a bar chart at the bottom of the recess area. -   12. a numbered area along the x-axis of the bar chart showing the     Fibonacci numbers in series. -   13. the playing area occupied by the bars of the chart, designated     as the staff base area. -   14. the empty area in the bar chart, designated as the stacking     area. -   15. the game screen on a computer, smartphone or tablet. -   16. tile assembly or play area. -   17. tile storage area. -   18. tile reception area. -   19. push button to get a tile. -   20. turn counter. -   21. thumbs up or down indicator. -   22. game card for Fibonacci number 8. -   23. game card for Fibonacci number 13. -   24. game card for Fibonacci number 21. -   25. game card for Fibonacci number 34. -   26. game card for Fibonacci number 55. -   27. game card for Fibonacci number 89. -   28. base game card for Fibonacci number 8. -   29. base game card for Fibonacci number 13. -   30. base game card for Fibonacci number 21. -   31. base game card for Fibonacci number 34. -   32. base game card for Fibonacci number 55. -   33. base game card for Fibonacci number 89. -   34. a bonus card.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT OF THE INVENTION

In the following descriptions and illustrations like reference numbers designate like parts throughout the figures.

FIG. 1 shows the Fibonacci series: 8, 13, 21, 34, 55 and 89 as a bar chart with the lowest Fibonacci number on the left. These bars occupy the base area of the chart.

FIG. 2 shows the bar chart modified to show a copy of the smaller of two adjacent bars on top of the larger of the two bars. The mathematical rule of the Fibonacci series, where each number in the series is equal to the sum of the two prior lower numbers, is shown visually in this figure.

FIG. 3 shows how the area in the chart of FIG. 1 above the base area can be stacked with bars, called tiles, having heights corresponding to the numbers in the Fibonacci series. In FIG. 3 there are 6 tiles in the base area at the bottom of each column and 15 tiles in the stacking area above the base area, for a total of 21 tiles. There are many combinations of tiles which exactly fill the stacking area. For each combination, the sum of the heights of the tiles within each vertical column is equal to the height of the tallest tile 89 said tiles in a single vertical column which add to 89 being called a group.

FIG. 4 shows the maximum number of tiles that can be placed exactly into the empty area in the chart of FIG. 1. There are 28 tiles in the empty area and a total of 34 tiles making the six groups.

FIG. 5 shows the minimum number of tiles that can be placed to exactly fill the stacking area in the chart of FIG. 1. There are 9 tiles in the stacking area giving a total of 15 tiles in the play area.

FIG. 6 shows six game pieces in one embodiment of the invention. Each game piece is in the form of a tile, one inch wide, ¼″ thick with a height proportional to the Fibonacci number assigned to the piece. The game piece or tile with the Fibonacci number of 89 is 6 inches tall. Tile 21 is therefore 21/89×6.0″=1.41 inches tall.

In a set of pieces, tiles of the same height are of the same color. Tiles identified with the numbers 8, 13, 21, 34, 55 and 89 are respectively labeled 1, 2, 3, 4, 5, 6 in FIG. 6 and are colored blue, yellow, green, black, red and purple. The tiles are made of wood or plastic and colored on all sides.

In this embodiment the set of game pieces, for a four player game, consists of four tiles 89 and 17 tiles each of tiles 8, 13, 21, 34, 55, giving a total of 89 tiles. Other embodiments could have a different number of tiles of each color and the set of pieces could be larger or smaller.

FIG. 7 shows one device for a player to randomly select a tile of a given color and number at the start of a turn. The arrow 7 is on a center pivot and is spun with a flick of the finger. The ring consists of six segments 8, each of a color corresponding to a numbered tile. When the arrow stops on a color, the player takes a tile of that color from the set.

An alternative device for selecting a tile is to roll a six sided die which has a different color on each face. The player takes a tile from the set having the color of the uppermost face of the die.

With the apparatus of FIG. 7 or with the rolling of a six sided die the probability of selecting a tile of a given color is the same for all tiles.

FIG. 8 shows a modified apparatus in which the relative probability of a tile of a given number and color being selected is changed by changing the relative sizes of the ring segments 9. This device allows a game to be made more or less difficult in a predetermined way.

FIG. 9 shows a game board 9, one for each player, on which game pieces are assembled into groups in accordance with a set of rules. In this embodiment the game board is 8.5 inches square and has a recessed area 10, which is ¼″ deep, 6.2″ wide and 6.2″ high. At the bottom of the recess is a bar chart 11, each bar is one inch wide and is colored to correspond to the tile of that height and number. The numbered area 12 at the bottom of the game board is not in the recessed area.

FIG. 9 shows the base area 13 and the stacking area 14.

A game for four players, in this embodiment, is played according to the following rules:

(a) Requirements:

-   -   Four game boards according to FIG. 9, one for each player     -   A set of 89 tiles consisting of four tiles 89 and 17 tiles each         of tiles 8, 13, 21, 34, 55     -   A six sided die, colored on each face to correspond to a         numbered tile         (b) Each player rolls the die once, in turn, and takes the         corresponding tile, one tile per turn         (c) Player places the tile on the corresponding bar in the base         area, if the space is available. If the bar has already been         filled the player puts the tile on one side for later play         (d) All six tiles must be placed on their bars in the base area         before tiles can be placed in the stacking area         (e) Tiles can be moved around in the stacking area, during and         between turns         (f) A player can forfeit rolling the die and return a tile to         the set as a turn

(g) Objective:

-   -   Be the first person to fill a game board with no tiles left over     -   Game finishes when one game board has been filled and the player         has no left over tiles         (h) Scoring (for a game when multiple rounds are played)     -   Score 100 for being the first to finish.     -   Other players score 5 for each completed vertical column or         group.

An embodiment of the game to be played on a computer, smartphone or tablet is now described.

FIG. 10 shows the appearance of the screen 15 in this embodiment. Screen 15 has a play area 16 into which tiles are dragged using a mouse or finger tip. A new tile appears in the reception area 18 when the player clicks or taps on button 27. Every time the player clicks on button 18, the number in box 20 increases by one.

When a tile appears in box 18 the player can choose to drag it into the play area 16 or drag it into storage area 17. The tiles appear smaller in box 18 and area 17 but increase in size when dragged into play area 16.

A player must complete the base area with all six tiles before dragging tiles into the stacking area. If the player gets a duplicate of a tile already placed in the base area, before the base area has been completed filled, the tile should be dragged into storage area 17 for later play.

Once the base area has been filled the player can start stacking tiles. Tiles can be dragged around in the stacking area during and between turns.

If a tile is dragged into a “legal” spot in the play area, it snaps into place in a column and the player gets a thumbs up from 20. A legal spot is a place where no tile is present and the tile does not result in a column of tiles taller than tile 89. The player can drag another tile into the play area 16 from storage area 17 or press button 19 to receive a new tile.

Unwanted tiles can be dragged off the screen and they disappear. However, the turn counter 20 increases by one for every tile removed. When the play area is completely full, all excess tiles have to be removed from the storage area by dragging them off the screen.

The objective is to completely fill the play area with tiles, with each column adding to 89, and to remove all unused tiles from the storage area 17, in the minimum number of turns.

Players can be given the choice of having tiles appear with or without numbers. In general it is easier to play the game when tiles are numbered since one can more easily do the mental arithmetic to find a tile combination that adds to 89. A screen button for this choice, with or without tile numbers, (not shown in FIG. 10) is then provided.

In another embodiment of the game, a player can select the degree of difficulty of the game to be played. A screen button for this choice (not shown in FIG. 10) is then provided.

In another embodiment, a digital clock is provided on the screen (not shown in FIG. 10) that starts running when button 19 is first clicked and stops running when play area 16 is full and storage area 17 is empty, signifying that the game is over.

An embodiment of the game which is played using a special pack of cards and no game board is now described.

In this embodiment a pack of 89 cards is used. This is appropriate for one to four players. FIG. 11, FIG. 12 and FIG. 13 show the cards.

FIG. 11 shows the faces of six playing cards 22, 23, 24, 25, 26 and 27 corresponding to the Fibonacci series, 8, 13, 21, 34, 55 and 89. The Fibonacci number appears on each card in the bottom left and top left corners. The bottom of each card has a colored area, which is different for each number, blue, yellow, green, black, red and purple. The height of the colored area on each card is in proportion to its Fibonacci number. Card 27 is number 89 and is a standard 3.5 inches high card. The height of the colored area on card 26 which is number 55 is 55/89×3.5=2.16 inches.

It will be apparent that if card 25 is placed on top of card 26 with the bottom of card 25 at the top of the colored section of card 26, the top of the colored section of card 25 will be 3.5 inches from the bottom of card 26. In other words a group of cards whose face values add to 89 can be stacked such that the combined colored areas are 3.5 inches high.

This feature is a visual aid in collecting groups of cards whose numbers add to 89.

A second set of cards shown in FIG. 12 and identified as 28, 29, 30, 31, 32 and 33 is used at the start of the game to create the base of each of the six groups to be collected. These are the base cards.

FIG. 13 shows a “bonus card” 34 which combines a base card for number 8 with two cards of number 13. This card, in effect, is three cards in one and provides three turns in one.

FIG. 14 shows the design on the back of every card. This is just one embodiment.

The pack of 89 special cards used in this embodiment for four players consists of:

-   -   4 each of base cards, 27, 28, 29, 30, 31, 32-24 cards     -   12 each of cards 21, 22, 23, 24, 25-60 cards     -   5 bonus cards 33-5 cards

Other embodiments can use a different number of cards in total and by type to make the game easier or more difficult.

In this embodiment a game for four players is played according to the following rules:

(a) Requirements:

-   -   A set of 89 cards as described above         (b) The pack of cards is shuffled and seven cards are dealt to         each player         (c) The balance of the pack is placed in the center of the table         and the top card is turned over alongside the pack         (d) Players hold their cards in hand, not visible to the other         players         (e) The first objective of every player is to collect and place         a set of base cards on the table in front of them from left to         right, 8, 13, 21, 34, 55 and 89         (f) The first player starts by picking up two cards from the         pack, or the overturned card and one card from the pack, and         then laying down all the base cards in his/her hand on the table         in order         (g) The player then throws away one card and it is the next         players turn         (h) Once a player has the entire base of six cards, additional         cards can be added (stacked) to any base card attempting to make         up a group where the numbers add to 89. The base card of 89         needs no additional cards         (i) Any completed group of cards is turned over showing the         image of FIG. 14         (j) Once a player has established the base line-up, cards can be         moved from group to group (but not a base card) during and         between turns         (k) A player can choose not to pick up any cards during a turn         and throw away one card         (l) Play stops when one player completes all six groups and has         no left over cards         (m) Scoring (for a game when multiple rounds are played)     -   Score 100 for being the first to finish     -   Other players score 5 for each completed group

The rules of the game, whether played with tiles, playing cards or on a computer device can be changed to create variety or to emphasize a particular feature of the Fibonacci series for educational purposes.

For example, to teach or to emphasize the way that each number in the Fibonacci series is equal to the sum of the two prior numbers, players could be required to first collect all of the base numbers and then have to collect and stack 34 on top of 55, 21 on top of 34, 13 on top of 21, and 8 on top of 13 before being free to fill the rest of the stacking area in any order. The pattern of the tiles which meet that requirement is shown in FIG. 2.

Another variation in the rules is to require that number 89 has to be placed first before any other number, then 55, then complete column 55 to make 89 with any combination of numbers, then 34, then complete 34 with any combination of numbers and so on, filling the play area from right to left.

Whether played with tiles, playing cards or on a computer, smartphone or tablet, the basic principles of this novel game are the same even if different rules are applied to add variety to the game.

A player that can quickly do mental arithmetic to find groups that total 89 has an advantage as does a player that can quickly visualize the color patterns that create a group of 89.

A player can develop a competitive advantage by memorizing the possible numeric combinations that add to 89 for a given base number. The number of possible combinations for each base number is as follows:

-   -   Base 8: 6 possibilities     -   Base 13: 7 possibilities     -   Base 21: 5 possibilities     -   Base 34: 5 possibilities     -   Base 55: 3 possibilities     -   Base 89: 1 possibility

These possibilities do not include alternative arrangements of pieces in a column within the group total of 89. Tiles can be moved up and down in the tile game and in the computer game. In the card game, cards can be placed in any order in a group. Tiles and cards can be moved between groups to facilitate completion.

Other embodiments of the game can use a modified Fibonacci series, which a purist would not call a Fibonacci series, such as:

-   -   2, 3, 5, 8, 13, 21

This sequence follows the rule that the numbers are equal to the sum of the two prior lower numbers. Number 1, which precedes number 2 in the series is not used. The sequence can be longer, for example have eight numbers:

-   -   2, 3, 5, 8, 13, 21, 34, 55

The advantage of using a modified series is that the numbers are easier for mental arithmetic and the game looks easier. All other aspects of the games remain the same.

The game is to be enjoyed but also provides a learning experience with respect to the Fibonacci series and its mathematical characteristics. The game provides exercises in memory and pattern recognition.

Having described the invention of the game in terms of several embodiments it will be apparent that longer or shorter sequences of a series could be used to create simpler or more elaborate games. Modifications to the probability of obtaining each numbered piece, for example by changing the distribution of numbered cards in a pack, can be introduced to further enhance the game. Other arrangements and improvements and changes in game rules can be made. For the sake of clarity and ease of understanding these have been omitted since it will be evident that they are properly within the scope of the claims. 

1-8. (canceled)
 9. A game for one or more players comprising the following apparatus: A set of game pieces of a predetermined number, each of said game pieces identified with a Fibonacci number, each Fibonacci number being one of the numbers in a predetermined Fibonacci series in which each said number is the sum of the two preceding lower numbers, said Fibonacci series having about six numbers; said game pieces being tile shaped, each of said tiles having the same width and thickness, each tile having a length in proportion to the Fibonacci number in said Fibonacci series, each tile of the same Fibonacci number having a corresponding color, said color being the same for all tiles having the same Fibonacci number; a game board for each player, said game board printed with a bar chart in a rectangular frame, the width of each bar equal to the width of said tiles, the height of said bar being the same as said tiles in ascending height order from left to right in the sequence of said Fibonacci series, the color of each said printed bar being the same as that of the corresponding said tile; a tile selection device selected from the group consisting of: (i) a die with each face of the die having a different color wherein each color is the same as one of said bars on said game board, (ii) a rotating arrow that stops on a colored segment of a ring, wherein each color is the same as one of said bars on said game board, said ring segments being of equal or unequal size, said segments of unequal size changing the probability of selecting a tile of a given color, (iii) a computer that generates the image of a tile with the click of a button said computer selecting a tile of each color with equal probability or unequal probability according to the computer settings chosen by said players in said game.
 10. A method of playing the game of claim 9 comprising the steps of: Providing each player with a game board according to claim 9, and providing a set of game pieces according to claim 9 accessible to each player and providing a tile selection device according to claim 9 accessible to each player; Players each take a turn in sequence, each said turn starting with the selection of a tile using said tile selection device, said player taking the corresponding tile from said set and placing said taken tile on the game board or alongside the game board as allowed by the rules of said game, each turn being completed with the placement of said taken tile; said rules require said taken tile to be placed on the game board on top of the printed bar corresponding to said taken tile Fibonacci number and color, or if said location has already been filled during a prior turn, said taken tile is placed alongside said game board unless all of the printed bar locations, denoted as the base area, have been filled in which case said taken tile can be placed in the area above the base area within said rectangular frame of said bar chart, denoted as the stacking area, said placement being contiguous with any previously placed tile; said rules allow said tiles placed in said stacking area to be moved into any location within said stacking area that is contiguous with any previously placed tile and within said bar chart but no tile can be placed in a location where some part of said tile extends beyond said bar chart rectangular frame; said rules allow a player who has filled the entire game board to return surplus tiles to the set, one surplus tile per turn without using said tile selecting device in said turn; said rules establish that the winning player is the player who is the first to completely fill the entire game board rectangle frame, including said base area and said stacking area with said taken tiles, with no tiles remaining.
 11. A card game for one or more players using the following apparatus: A pack of cards wherein each card in said pack has a face side and a back side, said back side being printed thereon with the same design on every one of said cards in said pack, said face side on a predetermined number of said cards in said pack being printed thereon with one Fibonacci number selected from a predetermined Fibonacci series of about six numbers wherein each said number in said Fibonacci series is the sum of the two preceding lower numbers, said pack having a predetermined number of cards printed with one or other of all of the Fibonacci numbers in said series, a predetermined number of said cards which are printed thereon with the same Fibonacci number being identified as base cards by having the word “base” printed on the face side of said base card in addition to said Fibonacci number printed thereon.
 12. A method of playing the card game of claim 11 comprising the steps of: Providing a pack of cards of claim 11; providing a set of rules stating the objective of said card game and the allowed steps each player can take during said player's turn and between each of said player's turns; the objective of said card game being to collect groups of said cards each of which starts with a base card of each Fibonacci number in said series, to which additional cards are added that are not base cards such that the sum of the numbers on said cards in said group add to the highest number in said Fibonacci series thus creating a completed group, with the winning player of said game being the player who creates one said completed group for each of said base cards of said Fibonacci series with no cards remaining in said winning players hand; said game is started with the steps of shuffling said pack, dealing the same number of cards, about seven, to each said player, the balance of said pack being placed face down in the center of the table and the top card upturned alongside, with each said player then taking a turn in sequence around the table; each turn of each said player comprises the steps of starting said turn by picking up two cards from said balance of the pack or one card from said balance of the pack and said top card alongside, adding said cards to the players hand, putting down on the table from said hand in front of said player any base cards but no more than one base card of each Fibonacci number, each said base card starting a group, adding cards to each base card once all base cards are put down, with the objective of creating said completed groups, ending said turn by discarding one card on to the upturned cards in the center of said table; said cards can be moved from one said group to another said group, during and between said turns, but said cards cannot be moved to or from said players hand except during said turns; a player can choose not to pick up said cards at the start of said turn and to end said turn by discarding one of said cards, this step being taken when said player has completed all said groups and is attempting to win said game by discarding all said cards remaining in said hand.
 13. A pack of cards according to claim 11 wherein the face side of each card in said pack is printed with a rectangle the base of said rectangle being located on the bottom of said card and the height of said rectangle on said card which has the highest Fibonacci number in said pack being the height of said card, completely filling said card, and the height of said rectangle on each of the other said cards being in proportion to the Fibonacci number on said card, said rectangles printed on each said card face being additional to the printed Fibonacci number thereon.
 14. A method for a single player to play the game of claim 9 on a computer, smartphone and tablet comprising the steps of: providing a screen appearance on said computer, said smartphone and said tablet, said screen appearance including a play area, a reception area, a storage area, a button and a counter, said computer, smartphone or tablet controlling the screen appearance and steps involved in playing said game; said play area showing a bar chart having six bars, the height of each bar proportional to a number in a Fibonacci series, said bars increasing in height from left to right, each of said bars being of a different color, said area under said bars in said bar chart being designated as the base area and the remainder of said play area being designated as the stacking area; a player starts a turn by tapping said button to introduce the image of a tile into said reception area, whereupon said counter increases by one, and then dragging said tile image out of said reception area; said tile image being randomly selected from a set of tile images stored in said computer, smartphone, or tablet each of said tile images corresponding in size and color to one of the numbers in said Fibonacci series and one of said bars in said bar chart; said player chooses during said turn whether to drag the tile image, using a mouse or finger tip, from said reception area onto said storage area, or onto said bar of the same size and color in said base area or onto said stacking area contiguous to a tile image placed in a prior turn; said player must receive and drag onto the base area all six tile images corresponding to the six bars in said bar chart, completely filling said base area, before said computer, smartphone or tablet allows a tile image to be dragged onto said stacking area; said player is allowed to move said tiles around in the stacking area and move said tiles from the base area or stacking area to the storage area; said player is allowed to discard an unwanted tile off the screen upon which action the counter increases by one since this action is a turn; said player's objective is to completely cover the base area and stacking area with said tiles with no tiles left over in the storage or reception area in the minimum number of turns as measured by said counter. 